Unstable time-delay systems and recycling systems are challenging problems for control analysis and design. When an unstable time-delay system has a recycle, its control problem becomes even more difficult. A control methodology for this class of systems is proposed in this paper. The considered strategy is based on the fact that if some internal system signals are available for measurement, then it will be possible to decouple the backward dynamics of the system and then a feedback controller could be designed for the forward dynamics. The key point for this strategy to be carried out is an asymptotic observer-predictor proposed to estimate these required internal signals. Necessary and sufficient conditions to assure convergence of this observer are given. After proving that the proposed control scheme tracks a step input signal and at the same time reject step disturbances, a procedure summarizing the methodology is provided. Robustness with respect to delay uncertainty and model parameters are also analyzed.

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Induction motors (IM) have been a fundamental part of industrial applications for over a century and the number of their applications continues to expand. A significant amount of the world’s total energy expense is consumed by this kind of motor. Hence, it is very important to increase the energy efficiency of these machines. Due to its good performance, field-oriented control (FOC) is the most common strategy to control IM. FOC requires references for stator current and rotor magnetic fluxes. For velocity regulation, a velocity reference is used instead of a stator current reference. However, at motor start-up or when a change of torque is required, it would be convenient for these references to be variable in order to reduce energy consumption. In this work, it is shown that this is indeed the case, and a technique to find optimal time-variable references for stator currents and magnetic rotor fluxes to reduce energy consumption is proposed. It is shown that, depending on the mechanical load, an energy reduction of 20–45% can be achieved.

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This work considers the problem of stabilization of a class of unstable first order linear systems subject to a large input-output time delay. Necessary and sufficient conditions are stated to guarantee the stability of the closed loop delayed system by means of a compensation scheme based on two static gains and an induced delay term. The proof of the main result is derived by considering a discrete time approach that, under adequate assumptions, allows to conclude the stability condition for the continuous time case.